Problem: The value of $\sqrt{107}$ lies between which two consecutive integers ? Integers that appear in order when counting, for example 2 and 3.
Consider the perfect squares near $107$ . [ What are perfect squares? Perfect squares are integers which can be obtained by squaring an integer. The first 13 perfect squares are: $ 1,4,9,16,25,36,49,64,81,100,121,144,169$ $100$ is the nearest perfect square less than $107$ $121$ is the nearest perfect square more than $107$ So, we know $100 < 107 < 121$ So, $\sqrt{100} < \sqrt{107} < \sqrt{121}$ So $\sqrt{107}$ is between $10$ and $11$.